The BLAST programs (BLASTP, PSI-BLAST, etc.) presently use offline computer simulations to give accurate estimates of statistical significance for sequence matches. This project has already speeded those offline computer simulations by a factor of 100-1000. Its eventual aim is to speed the simulations further, so they can be done online over the web. If the project is successful, BLAST users will then be free to use any scores and penalties they choose for matching sequences. There are two parameters in sequence matching statistics: the scale parameter lambda and the pre-factor k. We heuristically derived the new equation for scale parameter lambda. This equation can estimate lambda efficiently with high accuracy. In addition, we have proposed several new formulas for Gumbel pre-factor k based on the path reversal identity and the Poisson clumping heuristic. This formula also provides very accurate results. We also have explored edge effects on the statistics. Edge effects are present because real sequences have limited lengths appear as a correction term in an asymptotic expansion of the probability of sequence matching. This edge effect is likely to be more important in the statistics of matching with gaps than it was in the statistics of matching without gaps, because gapped matches tend to be longer, exhausting the sequences being matched more easily. We now have a working prototype program that calculates lambda and k in 1 second for a wide range of alignment parameters. At least two related publications are planned.